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1. Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.

1. Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 8741 Points
3 months ago
To convert the given trigonometric ratios in terms of cot functions, use trigonometric formulas We know that, cosec2A – cot2A = 1 cosec2A = 1 + cot2A Since cosec function is the inverse of sin function, it is written as 1/sin2A = 1 + cot2A Now, rearrange the terms, it becomes sin2A = 1/(1+cot2A) Now, take square roots on both sides, we get sin A = ±1/(√(1+cot2A) The above equation defines the sin function in terms of cot function Now, to express sec function in terms of cot function, use this formula sin2A = 1/ (1+cot2A) Now, represent the sin function as cos function 1 – cos2A = 1/ (1+cot2A) Rearrange the terms, cos2A = 1 – 1/(1+cot2A) ⇒cos2A = (1-1+cot2A)/(1+cot2A) Since sec function is the inverse of cos function, ⇒ 1/sec2A = cot2A/(1+cot2A) Take the reciprocal and square roots on both sides, we get ⇒ sec A = ±√ (1+cot2A)/cotA Now, to express tan function in terms of cot function tan A = sin A/cos A and cot A = cos A/sin A Since cot function is the inverse of tan function, it is rewritten as tan A = 1/cot A

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